Homeworks

Homework 1 Due September 10

Read Appendix A from the textbook.
Written part consists of 3 Questions and 3 Exercises.
Write solutions to Questions A.0 3, A.2 1, A.3 1.
Write solutions to Exercises A.4 8/9/10.
Questions and Exercises appear right after the corresponding chapter in the book. For example, Exercise A.4 9 is the exercise 9. that appears after Section A.4 in the Appendix 4.

Homework 2 Due September 17

Read Chapter 1 from the textbook.
Written part consists of 2 Questions and 4 Exercises.
Write solutions to Questions 1.2.3 (p.4), 1.4.2(p.8).
Write solutions to Exercises on p.12-13: 1.3.1, 1.5.1, 1.5.3, 1.6.4.

Homework 3 Due September 24

Read Chapter 2 from the textbook.
Written part consists of 2 Questions and 4 Exercises.
Write solutions to Questions 2.5.4(p.26), 2.6.1 (p.30).
Write solutions to Exercises on p.30-32: 2.1.4, 2.4.1, 2.4.7, 2.6.4.

Homework 4 Due October 1

Read Chapters 3-4 from the textbook.
Written part consists of 6 Exercises.
Write solutions to Exercises on p.46-47: 3.1.1(a-e), 3.2.3(a,b), 3.4.2, 3.4.5.
Write solutions to Exercises on p.58: 4.2.1(a,b), 4.3.3(i-iii).

Homework 5 Due October 8

Read Chapter 5 from the textbook.
Written part consists of 3 Questions and 3 Exercises.
Write solutions to Questions 5.2.2(p.66), 5.4.1, 5.4.3 (p.71).
Write solutions to Exercises on p.73-74: 5.1.4, 5.2.3, 5.4.2.

Homework 6 Due October 22

Read Chapter 6 from the textbook.
Written part consists of 3 Questions, 3 Exercises and 3 Problems.
Write solutions to Questions 6.2.3(p.82), 6.3.1(a,b,c)(p.83), 6.4.1 (p.86).
Write solutions to Exercises on p.89-90: 6.1.2, 6.4.1, 6.4.2.
Write solutions to Problems on p.91-92: 6-3, 6-5, 6-6.
Hint for Problem 6-3. Prove that:
` 0 < a_m -a_n < f(n)-f(m) for m>n.`
Remark for Problem 6-5. A sequence 1-1/n is bounded and increasing, but it does not have a maximum. Read Section 6.5 carefully.

Homework 7 Due October 29

Read Chapter 7 from the textbook.
Written part consists of 2 Questions and 4 Exercises.
Write solutions to Questions 7.2.3(p.100), 7.6.3(p.107).
Write solutions to Exercises on p.111: 7.4-7.5/2.,3.,4.,5.
Notation 7.4-7.5/... should not be confusing, when you look at the book.

Homework 8 Due November 5

Read Chapters 8, 9, 10.1 from the textbook.
Written part consists of 6 Exercises.
Write solutions to Exercises 8.1.1(b),(d),(f),(h) on p.123, 8.4.1 on p.124, 9.2.2, 9.2.3 on p.134, 9.4.1 on p.135, 10.1.6(a),(b) on p.148.

Homework 9 Due November 12

Read Chapters 10 and 11 from the textbook.
Written part consists of 4 Questions and 2 Exercises.
Write solutions to Questions 10.3.1(a)-(f) p.144, 10.4.1(a)-(c) p.147.
Write solutions to Questions 11.1.1 p.155, 11.3.2(a)(b) p.161.
Write solutions to Exercises 11.3.3(a)(b), 11.5.4. p.168.

Homework 10 Due November 19

Read Chapter 11 from the textbook.
Written part consists of 2 Questions and 4 Exercises.
Write solutions to Questions 11.4.3, 11.4.4(a)(b) p.165.
Write solutions to Exercises 11.3.1(a)(b), 11.4.1, 11.4.3, 11.4.4 p.167-168.

Homework 11 Due December 3

Read Chapters 12-13 from the textbook.
Written part consists of 2 Questions and 4 Exercises.
Write solution to Question 12.4.1 p.180.
Write solutions to Exercises 12.1.4(a)(b), 12.2.3 p.180-181.
Write solution to Question 13.2.4 p.187.
Write solutions to Exercises 13.4.1, 13.5.6(a)(b) p.193.
Note that in 13.4.1 f may be discontinuous, see the next exercise 13.4.2.

Homework 12 Due December 10

Read Chapters 14,15 (Sections 1 and 2 only),18 from the textbook.
Written part consists of 2 Questions and 4 Exercises.
Write solutions to Exercises 14.1.6(a)(b), 14.2.3 p.205-206.
Write solution to Question 15.1.1 p.211.
Write solution to Exercise 15.2.1(a)(b) p.218.
Write solution to Question 18.2.4 p.244.
Write solution to Exercise 18.3.1 p.248.